MIDDLE SCHOOL QUESTIONING VIGNETTE
TEACHER - So do we all understand how to find the area of a trapezoid?
Silence, some nodding, some looking around.
TEACHER - JaVaughn, are you good? Any questions?
JAVAUGHN – Wait, what? Oh, um, no.
TEACHER - Lucia?
LUCIA– Well, I guess I could use another example.
TEACHER - Okay, let’s try another one! Ethan, draw a trapezoid on the board and label its side
lengths.
ETHAN – Anything? (Teacher nods, Ethan draws a parallelogram with side lengths of 4 and 7, but
does not give a height.)
TEACHER – No, that’s not a trapezoid.
ETHAN – Well, you said anything.
TEACHER– Samantha, can you give us one?
SAMANTHA – (Samantha goes to the board and draws a traditional trapezoid with a slant height
of 4 and bases of 6 and 12.)
TEACHER – You meant to label the height 4, not this side. (Teacher corrects the drawing.) Okay,
well, first what do we do? We use our formula, right? What is the formula?
LUCIA- Something like b one plus b two times h and then all over 2.
TEACHER – Well, I guess that would work, but we usually write it like this, one half b one plus b
1
two times h. (Teacher writes the expression 2 (𝑏1 + 𝑏2 )ℎ on the board.)
TEACHER – So, what we do next. What numbers do we put in the formula?
(pause, no responses)
SAMANTHA (finally says the answer without being called on)– Put the 6 in for b one, the 12 in for
b two and the 4 in for h, then type it into your calculator and you get 36.
TEACHER – Does everyone agree? (pause) Does anyone disagree? (pause, some shake heads)
Okay, so our solution is 36 something, we could use inches squared, I suppose. Okay, that should
take care of any problems, right? Do problems 7-27 odd on page 432.
(pause)
TEACHER - Wait, note that #7 and 9 are sideways, so you just have to do turn the book over and
then do it the same way. Oh and 23, 25, and 27 are a little different because the sides come in
differently. We talked about those yesterday, but just skip them and we will do them together
tomorrow.
Illinois State Board of Education
SSOS Math Content Specialists Team